On a Discrete Version of the Mohr-Mascheroni Theorem


We introduce a new geometric tool called n-compass and show that the famous theorem of Mascheroni and Mohr remains valid if the traditional compass is replaced by the newly introduced tool.

Share and Cite:

M. Munteanu and L. Munteanu, "On a Discrete Version of the Mohr-Mascheroni Theorem," Applied Mathematics, Vol. 4 No. 11D, 2013, pp. 11-13. doi: 10.4236/am.2013.411A4002.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] L. Mascheroni, “Geometrie du Compas,” Monom, 1980.
[2] G. Mohr, “Euclides Danicus,” Copenhagen, 1928.
[3] N. Hungerbuhler, “A Short Elementary Proof of the Mohr-Mascheroni Theorem,” American Mathematical Monthly, Vol. 101, No. 8, 1994, pp. 784-797.
[4] A. Avron, “Theorems on Strong Constructibility with a Compass Alone,” Journal of Geometry, Vol. 30, No. 1, 1987, pp. 28-35. http://dx.doi.org/10.1007/BF01223260
[5] A. Avron, “On Strict Strong Constructibility with a Compass Alone,” Journal of Geometry, Vol. 38, No. 1-2, 1990, pp. 12-15. http://dx.doi.org/10.1007/BF01222890
[6] V. Pambuccian, “Axiomatizing Geometric Constructions,” Journal of Applied Logic, Vol. 6, No. 1, 2008, pp. 24-46.
[7] Z. Zhang, L. Yang and X. R. Hou, “What Can We Do with Only a Pair of Rusty Compasses?” Geometriae Dedicata, Vol. 38, 1991, pp. 137-150.
[8] V. J. Baston and F. A. Bostok, “On the Impossibility of Ruler-Only Constructions,” Proceedings of the American Mathematical Society, Vol. 110, No. 4, 1990, pp. 10171025.
[9] D. Fog, “Om Konstruktion Med Passeren Alene,” Mathematisk Tidsskrift A, 1935, pp. 16-24.
[10] V. S. Martynenko, “Mascheroni’s Theorem in Lobachevski Geometry,” Doklady Akademii Nauk Ukrainskoj SSR, Ser A, Vol. 1, 1982, pp. 22-27.

Copyright © 2021 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.